General axial response of stranded wire helical springs

The large static deflection of an axially loaded helical spring formed of a twisted strand of smooth circular wires is considered. Contact between the wires in the strand may or may not be maintained upon loading, depending upon the type of construction and the type of loading. It is found that the making or breaking of wire contact within the strand has a drastic ettect upon the extension and twist of a wire and upon the extension of the strand, but has practically no effect upon the twist of the strand, and only a moderate effect upon the overall response of the spring. Limited experimental data tend to verify the theory. It is found that a good engineering approximation for the axial stiffness of a twisted m-wire spring in which contact is maintained can be made by treating the spring as m untwisted helical wires acting independently, provided the strand twist is not too severe.     

Statically indeterminate contacts in axially loaded wire strand

This paper is concerned with the analysis of simple wire strands made from one layer of circular wires helically wrapped around a circular straight core wire. The undeformed configuration is the special case in which each of the surrounding helical wires touches its two adjacent neighbouring helical wires as well as touching the core wire. This forms a statically indeterminate contact problem. A simple finite element model is developed to analyse this situation. Numerical results show that contacts can occur simultaneously at all possible contact points when the strand is subjected to extension with both ends fixed against rotation.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命,本文利用参数化方法建立了精细化的钢绞线拉索有限元模型,包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况,并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大,中心处几乎没有相对滑动,微动疲劳的初始裂纹萌生点位于接触区域边缘;经不同区域子模型分析比较,在轴向循环荷载作用下,外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤;在横向位移循环荷载作用下,同层钢丝因位置角度不同而产生了较大的疲劳特性差异,且相比轴向循环拉伸,该工况下最不利单丝的微动疲劳寿命更低;与非接触区域相比,接触区的疲劳寿命大幅降低,微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

The mechanical behavior of a wire rope with an independent wire rope core

A new model for simulating the mechanical response of a wire rope with an independent wire rope core is presented. The rope is subjected to both an axial load and an axial torque. In contrast with previous models that consider the effective response of wound strands, the present model fully considers the double-helix configuration of individual wires within the wound strand. This enables to directly relate the wire level stress to the overall load applied at the rope level. The model assumes a fiber response of individual wires. Two alternative kinematics of the wires are considered, and are used to predict the elastic response of the rope. The postulated kinematics are theoretically validated and the predicted rope response is in agreement with new experimental data. The new model enables the extraction of the stress at the wire level that can be used in turn to estimate global features of the rope such as force interaction between wires, rope stiffness, strength, and fatigue life.     

Response of a wire rope strand to axial and torsional loads: Asymptotic modeling of the effect of interwire contact deformations

The refined discrete mathematical model of a simple helical wire rope strand is developed. The effect of the transverse contraction of the wire strand through Poisson’s ratio and also through local contact deformations (wire flattening) has been studied in detail. In order to express the interwire contact deformation in terms of the parameters describing the strand deformation, we formulate a two-dimensional model interwire contact problem. The interwire contact interaction is treated as a frictionless unilateral plain strain problem. The nonlinear model interwire contact problem has been solved by the method of matched asymptotic expansions. The constitutive equations for a helical wire rope strand, which take into account both the Poisson’s ratio effect and the effect of contact deformation, are obtained in a closed form.     

服役导线的力学性能退化研究

为更清楚地了解阳江35kV服役导线的运行状态,从分析导线断线原因出发,通过对老旧导线的单丝断裂强度、弹性模量、应力应变曲线、拉断力、抗拉强度等综合指标的测试与分析,研究服役导线的力学性能,由试验结果得出:35kV老旧导线钢芯的直径变化对于架空导线的外径变化有直接的影响,老旧导线的铝线直径变化较小,其外径增大1.67%~4.24%;钢单线的拉断应力仍能达到标准中规定值的106%,且伸长率也满足要求;部分铝线的抗拉强度低于95%;绞线拉断力仍能达到95%的计算拉断力。但是相同规格下的老旧导线的抗拉强度比新导线的抗拉强度低2%~18%。结果表明:阳江地区服役三十年以上的老旧导线在力学性能上仍能继续承载。     

基于ASME应变限制准则的小冲杆试验等效断裂应变

为更清楚地了解阳江35kV服役导线的运行状态,从分析导线断线原因出发,通过对老旧导线的单丝断裂强度、弹性模量、应力应变曲线、拉断力、抗拉强度等综合指标的测试与分析,研究服役导线的力学性能,由试验结果得出：35kV老旧导线钢芯的直径变化对于架空导线的外径变化有直接的影响,老旧导线的铝线直径变化较小,其外径增大1.67％~4.24％;钢单线的拉断应力仍能达到标准中规定值的106%,且伸长率也满足要求;部分铝线的抗拉强度低于95%;绞线拉断力仍能达到95%的计算拉断力。但是相同规格下的老旧导线的抗拉强度比新导线的抗拉强度低2%~18%。结果表明：阳江地区服役三十年以上的老旧导线在力学性能上仍能继续承载。     

Analytical solutions for bending and flexure of helically reinforced cylinders

There has been a great deal of interest in the problems of modelling cables and ropes. A recent review by Cardou and Jolicoeur [Appl. Mech. Rev. 50 (1997) 1] considers the modelling of a cable which consists of a central core surrounded by one or several helically wound wire layers. One approach has been to consider the deformations of an individual helical wire and to synthesise the model of a cable by using contact conditions between the various wires. Other authors have adopted a continuum approach regarding each layer as a transversely isotropic material whose principal direction is along a helix surrounding the central axis of the cable. In each layer the helix angle is constant so that, when referred to cylindrical polar co-ordinates, the cylinder has a constant stiffness matrix in each layer. The intention in this paper is to use the continuum approach and describe the analytical solutions that govern the simple bending, flexure, or bending under a uniform load, of an anisotropic elastic cylinder consisting of a single material of this type. The extension of this work to a composite cylinder consisting of several concentric layers, surrounding a central core, which are either bonded together or make a frictionless contact, is briefly described.     

Superelastic shape memory alloy cables: Part II – Subcomponent isothermal responses

This paper constitutes the second part of our experimental study of the thermo-mechanical behavior of superelastic NiTi shape memory alloy cables. Part I introduced the fundamental, room temperature, tensile responses of two cable designs (7 × 7 right regular lay, and 1 × 27 alternating lay). In Part II, each cable behavior is studied further by breaking down the response into the contributions of its hierarchical subcomponents. Selected wire strands were extracted from the two cable constructions, and their quasi-static tension responses were measured using the same experimental setup of Part I. Consistent with the shallow wire helix angles in the 7 × 7 construction, the force–elongation responses of the core wire, 1 × 7 core strand and full 7 × 7 cable were similar on a normalized basis, with only a slight decrease in transformation force plateaus and slight increase in plateau strains in this specimen sequence. By contrast, each successive 1 × 27 component (1 × 6 core strand, 1 × 15 strand, and full cable) included an additional outer layer of wires with a larger number of wires, greater helix radius, and deeper helix angle, so the normalized axial load responses became significantly more compliant. Each specimen in the sequence also exhibited progressively larger strains at failure, reaching 40% strain in the full 1 × 27 cable.Stress-induced phase transformations involved localized strain/temperature and front propagation in all of the tested 7 × 7 components but none of the 1 × 27 components aside from the 1 × 27 core wire. Stereo digital image correlation measurements revealed finer features within a global transformation front of the 1 × 7 core strand than the 7 × 7 cable, consisting of an staggered pattern of individual wire fronts that moved in lock-step during elongation. Although the 1 × 27 multi-layer strands exhibited temperature/strain localizations in a distributed pattern during transformations, the localizations did not propagate and their cause was traced back to contact indentations (stress concentrations) arising from the cable’s fabrication. The normalized axial torque responses of the multi-layer 1 × 27 components during transformation were distinctly non-monotonic and complex, due to the alternating handedness of the layers. Force and torque contributions of individual wire layers were deduced by subtracting 1 × 27 component responses, which helped to clarify the transformation kinetics within each layer and explain the unusual force and torque undulations seen in the 1 × 27 cable response of Part I.     

A structural model for high pressure helical wire-wound thermoplastic hose

This paper develops a model for a specific type of hose construction designed to withstand very high operating pressures. The model is based on a model previously developed by Entwistle and White (Int. J. Mech. Sci. 19 (1977) 193) with two significant modifications. Firstly the compressible inner core is included in the model using Lamé's thick walled cylinder theory. Secondly the model allows for the squeezing effect on wires when a hose gets shorter under pressurisation. The model calculates whether the wires in a particular layer will be squeezed together and when this occurs, the behaviour is modelled using Hertzian contact theory. The governing equations are solved using a minimising Newton Raphson technique. Model predictions are compared with experimental results obtained for pressure deformation response in terms of hose axial strain and wire strain and show good agreement. Considerable hysteretical behaviour is seen in the hose axial strain and it is suggested that this may be due to the twisting contact movements between different layers and as such may be a good indicator of the amount of fretting taking place. It is also suggested that, when a hose is designed to get shorter on pressurisation, length change may be a good indicator of manufacturing quality in terms of wire packing efficiency.     

定、变载弯曲疲劳钢丝绳失效机理对比研究

为对比揭示定、变载弯曲疲劳钢丝绳断裂机理及磨损演化特性,运用自制钢丝绳弯曲疲劳试验机开展钢丝绳定载、变载弯曲疲劳试验,通过人工拆股统计法和VW-9000系列高速度数码显微系统对比研究钢丝绳断丝分布、断丝数、断口和磨痕形貌等断裂机理,对比分析钢丝绳未断钢丝和断丝的磨痕尺寸演化特性. 结果表明:与钢丝绳定载弯曲疲劳相比,变载弯曲疲劳钢丝绳断丝出现较晚,芯股、螺旋股外层断丝数分别较多、较少,芯股外层钢丝断口挤压变形较大,芯股各层钢丝断口裂纹扩展区占比较低,芯股和螺旋股的各层钢丝磨痕尺寸总体较小,钢丝绳更易达到报废水平.      

微动频率对钢丝拉扭复合微动腐蚀疲劳行为影响研究

拉扭复合微动腐蚀疲劳是深井提升钢丝绳主要失效形式之一,深井提升钢丝绳振动频率决定钢丝间微动频率,直接影响钢丝拉扭复合微动腐蚀疲劳机理和损伤程度,进而制约深井提升钢丝绳服役安全性. 本文作者通过自制钢丝拉扭复合微动腐蚀疲劳试验机开展了酸性电解质溶液中钢丝拉扭复合微动腐蚀疲劳试验,通过钢丝切向力-位移幅值和扭矩-扭转角滞后回线分析了拉扭复合微动腐蚀疲劳过程中钢丝间接触状态及轴向和扭转方向钢丝耗散能,运用扫描电子显微镜和三维白光干涉表面形貌仪考察了拉扭复合微动腐蚀疲劳过程中钢丝磨痕形貌和磨损深度轮廓特性,采用X射线三维成像系统揭示了钢丝拉扭复合微动腐蚀疲劳裂纹扩展演化规律,通过电化学分析仪分析试验后钢丝Tafel极化曲线和阻抗谱以探究钢丝电化学腐蚀倾向和耐腐蚀性,揭示了微动频率对拉扭复合微动腐蚀疲劳过程中钢丝间接触状态、钢丝耗散能、微动磨损机理、疲劳裂纹扩展演化和疲劳寿命、电化学腐蚀倾向和耐腐蚀性的影响规律. 结果表明:在拉扭复合微动腐蚀疲劳过程中,随着微动频率的增加,钢丝间由完全滑移和部分滑移混合状态变为完全滑移状态,钢丝扭矩-扭转角滞后现象削弱,钢丝切向力-位移幅值和扭矩-扭转角滞后回线对应的耗散能均总体降低,钢丝间摩擦系数和钢丝磨损深度均降低,钢丝磨损机理均为磨粒磨损、黏着磨损、疲劳磨损和腐蚀磨损,钢丝最大裂纹深度和裂纹扩展速率均降低,疲劳寿命增加,钢丝电化学腐蚀倾向下降和耐腐蚀性增强.      

Discrete element modelling of pebble beds: With application to uniaxial compression tests of ceramic breeder pebble beds

In this paper, a discrete element simulation scheme for pebble beds in fusion blankets is presented. Each individual pebble is considered as one element obeying equilibrium conditions under contact forces. We study not only the rearrangement of particles but also the overall behaviour of an assembly under the action of macroscopic compressive stresses. Using random close packing as initial configurations, the discrete element simulation of the uniaxial compression test has been quantitatively compared to experiments. This method yields the distribution of the inter-particle contact forces. Moreover, the micro-macro relations have been investigated to relate the microscopic information, such as the maximum contact force and the coordination number inside the assembly, to the macroscopic stress variables.     

干燥和酸性条件下钢芯铝绞线磨损特性研究

在自制导线微动磨损试验机上考察了钢芯铝绞线在干燥和酸性2种典型气候条件下的微动磨损行为,利用扫描电子显微镜和铁谱显微镜分析了试样导线内外层线股接触区的表面形貌和磨损微粒的形貌、尺寸等.结果表明：2种试验条件下靠近线夹处的导线磨损机理主要为黏着和疲劳剥落,中间导线段的磨损机理主要为黏着和磨粒磨损,酸性条件下导线内还存在明显的腐蚀磨损.     

Experimental and Analytical Investigation of Carbon Fiber Cable Vibration Damping

For structures deployed in space using cables where vibration damping is critical for structural stability, cable damping is significant to structural performance. To provide a better understanding of damping mechanism of carbon fiber cables, this paper describes the tests of cable damping under different experimental configurations (different cable length, tension and type), and presents an analytical method for modeling and therefore predicting cable damping. The method is developed using simplified but physically realistic assumptions on material constitutive properties and geometric compatibility conditions, and considered the contact forces and friction between helical wires. The results of the proposed method and several related issues are discussed and compared with those from experiments. These results show that the proposed method is useful and applicable for predicting cable damping value and its variation with cable tension, length and type of the cables.     

Measurement of Strain/Load Transfer in Parallel Seven-wire Strands with Neutron Diffraction

The elastic strains induced in the constituent wires of parallel wire strands under tensile loading were measured using neutron diffraction. The elastic strains carried by the individual wires depended very strongly on the boundary conditions at the grips and on radial clamping forces. The friction forces between the wires were quite significant and should not be neglected in analytical or numerical formulations of strain partitioning in parallel wire cables.     

A Theoretical Study on Nonlinear Bending of Wires

The nonlinear bending of thin wires is a challenging topic in several applications where the final geometry of the wire after bending and springback has to be known. Typical examples are tyre manufacturing, helical spring design, spectacles frames. In order to develop analytical models able to set bending parameters for a required final shape of the wire, both account material behaviour (during the loading and unloading phases with springback effect) and geometrical nonlinearity have to be considered. In the case of plates bending, many analytical and numerical models are available in the literature, offering an accurate solution to this problem. However, the bending of thin wires could still be the subject of discussion and research. In this paper a new analytical model was developed, starting from the models available in the literature, in order to provide the designer with a simple model to predict the final shape of a wire by using mathematical codes. The model allows to predict with a higher level of accuracy the final shape of wires having different cross-sections after nonlinear bending. Since Bernoulli’s hypothesis is assumed, the model can be used in all the applications where the material behaviour of the wire guarantees that plane cross sections of the wire will remain plane after rotation due to bending, with negligible errors from the engineering point of view.     

Propagation of a longitudinal pulse in wire ropes under axial loads

Measurements of the velocity of propagation of longitudinal pulses in wire ropes as a function of applied tension are reported. Twelve 3/8-in.-diam cables are investigated which differ in configuration, i.e., number of wires per strand and number of strands, and in the material from which the wires and the core are fabricated. The velocity of longitudinal waves is found to increase with increasing tension, approaching the velocity in a solid steel bar as the applied load is increased toward the failure load of the wire rope. The material from which the wires are fabricated and the number of strands, rather than the number of wires in a strand or its core material, appear to significantly affect the velocity of longitudinal pulses.     

非圆截面弹性细杆的螺旋线平衡及稳定性

本文研究端部受力和力矩作用，且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系，并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明，松弛状态下弹性杆可处于螺旋线状态，直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。     

Effective macroscopic adhesive contact behavior induced by small surface roughness

In this paper we study a model contact problem involving adhesive elastic frictionless contact between rough surfaces. The problem's most notable feature is that it captures the phenomenon of depth-dependent-hysteresis (DDH) (e.g., see Kesari et al., 2010), which refers to the observation of different contact forces during the loading and unloading stages of a contact experiment. We specifically study contact between a rigid axi-symmetric punch and an elastic half-space. The roughness is represented as arbitrary periodic undulations in the punch's radial profile. These undulations induce multiple equilibrium contact regions between the bodies at each indentation-depth. Assuming that the system evolves so as to minimize its potential energy, we show that different equilibrium contact regions are selected during the loading and unloading stages at each indentation-depth, giving rise to DDH. When the period and amplitude of our model's roughness is reduced, we show that the evolution of the contact force and radius with the indentation-depth can be approximated with simpler curves, the effective macroscopic behavior, which we compute. Remarkably, the effective behavior depends solely on the amplitude and period of the model's roughness. The effective behavior is useful for estimating material properties from contact experiments displaying DDH. We show one such example here. Using the effective behavior for a particular roughness model (sinusoidal) we analyze the energy loss during a loading/unloading cycle, finding that roughness can toughen the interface. We also estimate the energy barriers between the different equilibrium contact regions at a fixed indentation-depth, which can be used to assess the importance of ambient energy fluctuations on DDH.